A widely used type of acoustic headset includes earpieces carried at first ends of a pair of sound-transmitting tubes, and a one-piece frame to hold the earpieces in place against the wearer's outer ears and to shape the tubes conveniently alongside the wearer's face. In the known headsets, there are two rigid arms in the form of elongated channels for supporting the earpieces, the arms being carried on resilient portions of the frame. The arms move angularly apart and then toward each other when the headset is being put on, thus fitting different persons differently. Moreover, the resilient support for the arms which is primarily intended to provide gentle bias of the earpieces against the ears must additionally be firm enough to bear the weight of the arms, a weight that changes when the wearer moves his head from time to time. Slight changes in attitude and in pressure of the earpieces can develop discomfort in some individuals where the listening period is prolonged.